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Finding derivative of x^x using limit definition

  1. Jul 10, 2015 #1
    I am trying to find the derivative of x^x using the limit definition and am unable to follow what I have read. Can someone help me understand why lim [(x+h)^h -1]/h as h ---> 0 = ln(x). This part of the derivatio
     

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  2. jcsd
  3. Jul 10, 2015 #2

    phion

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    Gold Member

    Try using the fact that [itex]e^{ln(x)}=x[/itex]
     
  4. Jul 17, 2015 #3
    Limit (a∧h) = 1 + h×log(a)/1! + ((h×log(a))∧2)/2! + ....
    h→0

    For the steps performed on the right side , use , as already said , x = e∧log(x) ,
    and

    Limit (log(1+h)) = h - (h∧2)/2 + (h∧3)/3 - ....
    h→0

    *Log is taken to base e .
     
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